The study of DFT from the perspective of para-Hermitian geometry, in settings more general than the flat para-Kähler case,
was further developed in [1]} and [2]}, [3]}, [4]}, [5]}, and also in several subsequent works,
being currently an active research area.
(Early considerations of the relationship between para-Hermitian structures and T-duality can be found in [6]}.)
A particularly important difference between Hermitian and para-Hermitian geometry is that the
eigenbundles of an almost-complex structure are complex conjugates of each other,
while those of an almost para-complex structure are independent.
As a consequence, the integrability properties of a para-Hermitian structure can be
split into separate questions about the involutivity of each eigenbundle, so one can talk about
“half-integrability”.
We will see that this is especially important in general relativity and its connection with twistor structures.
